# Introduction to ANOVA

Looking for ANOVA Assignment Help? You are at Right Place. Anova is the abbreviation for Analysis of Variance. It was developed by Robert Fisher. Its application was first published in the early 1920’s. Since then it has proved instrumental in providing significant statistical conclusions in various research. ANOVA is a collection of statistical tools which helps in drawing a significant inference between different groups of data. ANOVA aims at comparing and proving that the means of different data sets are equal.

The ANOVA test determines the significance of the difference between the means of three or more groups.Before delving into Analysis of Variance, it is imperative to have a fundamental understanding of standard deviation, variance, and hypothesis testing. Standard deviation and Variance are also known as measures of dispersion. They determine the variation of individual values from the mean within a data set. Courseworktutors Inc provides ANOVA Assignment Help on your queries relating to ANOVA Questions.

## Basics for Anova

Below is an overview of some of the basic concepts which will help in better understanding ANOVA.

**Standard deviation** is an estimate quantifying how each data set is different from the mean observation. It is expressed in the same unit as the mean.

**Variance** is the square of standard deviation. A higher variance denotes that the data points are located further away from the mean. Unlike standard deviation, it is expressed in squared units. Since this is expressed in a standardized form, Variance is more useful when comparing results from diverse sets of data.

**Hypothesis testing** is used to determine if the results from the analysis of a sample are reflective of the entire population. It consists of two theories: a null hypothesis and an alternative hypothesis. The null hypothesis is the statement which is being tested whereas an alternative hypothesis is an outcome which is expected to be concluded as true. The end result of a Hypothesis test is either to ‘reject the null hypothesis’ or ‘fail to reject’ thereby impacting the alternative hypothesis.

**The T-Test** is used to analyze the means of two samples through statistical examination. It is, however, different from the ANOVA, since ANOVA examines the equality of the mean for more than two samples.

** F-Test** is a statistical test which assists in identifying the model that best fits the population from which the sample data has been picked up.

### Working of ANOVA

Calculation of ANOVA is a lengthy procedure and might seem to be complex due to the immense number of samples and therefore Students can take ANOVA Assignment Help. However, when broken down into separate steps, a pattern of analysis becomes evident.

Consider a data set which shows marks of 5 students (s1 to s5) over a period of time. The students are the same. One group shows the marks in 10th (g1). The second group when they are in 12th (g2) and the third in the final year of graduation (g3). If represented in a tabular format, they would appear as below.

**Step 1** Calculate mean of each group i.e. 10th, 12th and graduation (Mean (g1), Mean (g2) and Mean (g3)

**Step 2** calculate Standard deviation [SD(g1), SD(g2), SD(g3)] and variance [Var(g1), Var(g2), Var(g3)] of each group.

** Step 3** calculate Grand mean, based on mean values of group 1, 2 and 3 (Grand Mean)

**Step 4** use the grand mean and calculate the difference from each data point (v1 to v15). Determine the square of each value and calculate the sum total. This is termed as Sum of Squares total.

**Step 5** Calculate Sum of Squares between. This is the sum of squares of mean of each group from the grand mean (ie [n*(Mean(g1) – Grand mean)2 + n*(Mean(g2) – Grand Mean)2 + n*(Mean (g3) – Grand Mean)2 ] where n is the number of samples in each group. This sample size is the 5 students in each group.

**Step 6** Sum of squared errors = Sum of squares total – the sum of squares between. This value can be verified by an alternative method. The cumulative value of Sum of squares of each group from its own mean should be the same as [Sum of squares total – sum of squares between]

**Step 7** Create ANOVA table and calculate degrees of freedom based on the number of groups (K = 3 groups) and total sample size (n = 3 groups and 5 observations each, i.e., a sample size of 15). Calculate mean square and F-ratio using ANOVA Table.

**7(a)** Mean Square between = Sum of Squares between / (k-1) Mean Square error = Sum of Square error / (n-k)

**7(b)** F Ratio = (Mean Square between )/ (Mean Square error)

**Step 8** Based on the values of F statistic we can conclude the hypothesis and “reject” or “fail to reject” the null hypothesis .

### Assumptions on ANOVA Assignment Help

There are certain underlying assumptions to the ANOVA computation. These assumptions can be listed as follows

1. All of the samples are independent of each other. The selection of samples within the entire population is random and not related to other samples.

2. The population is normally distributed

3. The population exhibits ‘homoscedasticity, ’ i.e., the variances of the populations are equal or homogeneous.

### Conclusion and Practical application

The entire procedure of ANOVA seems incredibly complicated; it is to be kept in mind that it compares multiple observations from many groups of data. In the above. Since the process is interwoven with each and every data set repeatedly, it drastically reduces the chance of statistical error. ANOVA is widely used in manufacturing, healthcare, financial services, etc. It is also a commonly used tool in Six Sigma.

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